Here we compile a brief self-contained review that we wish had existed when we first entered the field [1]}.
In what follows in the frame work of generalized Zwanzig approach we study a number of nano-size quantum systems.
Since our work is primary about physics (and only then how it can be modeled theoretically) it is worth to note first
what are physical systems we have in mind. Our topic is nano-size quantum objects, possessing discrete vibrational energy
spectra. Such objects are carbon nano-tubes, graphene flacks, metallic clusters, some large organic molecules or their clusters.
Typical feature (relevant for everything what follows in the paper) of such systems is that their vibrational spectra
are discrete and characteristic inter-level spacing \({\bar{\Delta }}\)  is on the order of \(0.1 \, -\, 10\, cm^{-1}\) .
This value of \({\bar{\Delta }}\)  is translated into the pico-second time scale for the periods of the recurrence cycles
\(T = \frac{2\pi }{c {\bar{\Delta }}} \simeq 10^{-10} \, -\, 10^{-12}\, s\, ,\) 
